# Book:B. Noble/Numerical Methods 2: Differences, Integration and Differential Equations

## B. Noble: Numerical Methods 2: Differences, Integration and Differential Equations

Published $\text {1964}$, Oliver and Boyd Ltd.

### Contents

VII. FINITE DIFFERENCES AND THE APPROXIMATE REPRESENTATION OF FUNCTIONS
7.1 Introduction
7.2 Finite difference tables
7.3 The use of differences in detecting errors
7.4 The differences of a polynomial
7.5 The approximate representation of functions
Examples VII
VIII. POLYNOMIAL INTERPOLATION
8.1 Introduction
8.2 Errors in polynomial interpolation
8.3 Aitken's method of interpolation by linear crossmeans
8.4 Newton's divided-difference interpolation formula
8.5 The Gregory-Newton and the Gauss formulae
8.6 The Everett, Bessel, and Stirling formulae
8.7 Practical interpolation using differences
Examples VIII
IX. NUMERICAL INTEGRATION AND DIFFERENTIATION
9.1 Introduction
9.2 The trapezoidal rule and Simpson's rule
9.3 Error estimation: Simpson's rule in hand and automatic computing
9.4 The treatment of singularities
9.5 Gaussian formulae
9.6 Central difference formulae
9.7 Numerical differentiation
Examples IX
X. ORDINARY DIFFERENTIAL EQUATIONS
10.1 Introduction
10.2 Elementary considerations
10.3 Error estimation when solving differential equations numerically
10.4 Programming the numerical solution of differential equations
10.5 Runge-Kutta formulae
10.6 Predictor-corrector methods
10.7 Errors and stability
10.8 A comparison of methods
10.9 Second-order equations
10.10 Two-point boundary conditions
Examples X
XI. PARTIAL DIFFERENTIAL EQUATIONS
11.1 Introduction
11.2 The heat conduction equation
11.3 Laplace's equation
Examples XI
INDEX